The \(\ell \) -th derivative of the generalized hypergeometric function
\({_pF_q}({\bf a}; {\bf b}; sx)\)  is given by [1]}:
\(\frac{{\rm \,d}^\ell }{{\rm \,d}x^\ell }{_pF_q}({\bf a}; {\bf b}; sx) = s^\ell \frac{({\bf a})_\ell }{({\bf b})_\ell }{_pF_q}(\tilde{{\bf a}}; \tilde{{\bf b}}; sx)\) 
